This is given the fact that they are opposite each other on the diagram of the two intersecting lines. That they are opposite in this way implies that they are equal in size. (They are like a mirror image of each other, if you imagine a mirror placed between them). Since they are equal we can say that they are congruent as congruent is another way of saying equal or identical.

Since m1 and m3 are equal, we can equate the two expressions in x defining each one, giving an equation in the variable x:

3x + 4 = x + 10

Using the subtraction property of equality, which is that equality is maintained when the same amount is subtracted from both sides of the equation, this implies that

1) subtracting x from both sides gives us

3x + 4 - x = x + 10 - x, leading to

2x + 4 = 10

2) Similarly, subtracting 4 from both sides gives us

2x +4 - 4 = 10 - 4, leading to

2x = 6

Then, using the division property of equality, which is that equality is maintained when both sides of the equation are divided by the same amount, this implies that